- #1

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## Homework Statement

Prove [itex] \sin{10} [/itex], in degrees, is irrational.

## Homework Equations

None, got the problem as is.

## The Attempt at a Solution

Im kinda lost.

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- Thread starter SrEstroncio
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- #1

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Prove [itex] \sin{10} [/itex], in degrees, is irrational.

None, got the problem as is.

Im kinda lost.

- #2

STEMucator

Homework Helper

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## Homework Statement

Prove [itex] \sin{10} [/itex], in degrees, is irrational.

## Homework Equations

None, got the problem as is.

## The Attempt at a Solution

Im kinda lost.

Okay, are you familiar with proof by contradiction?

Start by contradicting the statement :

Suppose that sin(10) is irrational.

- #3

Dick

Science Advisor

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## Homework Statement

Prove [itex] \sin{10} [/itex], in degrees, is irrational.

## Homework Equations

None, got the problem as is.

## The Attempt at a Solution

Im kinda lost.

Let x=sin(10). You'll want to find a polynomial x satisfies and show it has no rational root. Hint: sin(30)=1/2=sin(10+10+10).

- #4

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I should suppose sin(10) is rational, if i am to contradict the statement, shouldnt i?

- #5

jedishrfu

Mentor

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next step...

- #6

Dick

Science Advisor

Homework Helper

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I should suppose sin(10) is rational, if i am to contradict the statement, shouldnt i?

Zondrina's hint contains nothing of any real substance to start solving the problem. Mine does. I suggest you start trying it.

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